Offline somerled

  • *
  • Posts: 112
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #40 on: November 04, 2019, 03:46:55 PM »
If you want real chaos then investigate the effect of chaos theory and the n-body problem associated with the orbits in the solar system model .
Are you really arguing that a 10-body problem of the solar system is more chaotic than the 10^44 - body system that is the atmosphere? Really?
Case in point - I can easily predict the orbits of all of the planets by numerically solving the n-body equation with a computer, and very accurately predict their positions for at least the next 100 years. Meanwhile the weather report can't even predict with 99% accuracy whether it's going to rain tomorrow.

You are not just a clown - you are the entire circus.

You should be aware that the "solar system " contains hundreds of bodies not just ten . This solar system is supposed to be part of a universe consisting of countless bodies - all in motion interacting through that magical force of attraction between masses . Chaotic indeed .

Planetary orbits are predictable through observation , always have been .

Meteorologist Edward Lorenz stumbled upon chaos theory while trying to predict weather patterns with his computer - read up on it .Thing about computers - put crap in , get crap out . 



*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #41 on: November 05, 2019, 08:03:02 PM »
You should be aware that the "solar system " contains hundreds of bodies not just ten . This solar system is supposed to be part of a universe consisting of countless bodies - all in motion interacting through that magical force of attraction between masses . Chaotic indeed .

Planetary orbits are predictable through observation , always have been .

Meteorologist Edward Lorenz stumbled upon chaos theory while trying to predict weather patterns with his computer - read up on it .Thing about computers - put crap in , get crap out .
Hundreds? The Solar System contains at least hundreds of thousands, more depending on how you define it.
Let's say there are 1 trillion bodies (1e12) in our solar system. There are around 100 billion stars (1e11) in our galaxy. That means if you put all of the galaxies in the observable universe together (1e12), you get a 1e34-body system, which is 10,000,000 times less than there are particles in our atmosphere.

Both are chaotic, n-body systems with very high n, but you seem to be suggesting that the solar system is highly chaotic and that the atmosphere isn't chaotic. Sorry if I misunderstood.

Planetary orbits are predictable through numerical simulations.
Please tell me where asteroid 2003 Harding (6559 P-L) will be in 50 years through "observation". Tell me where its perihelion is, tell me its orbital eccentricity. You can't, but numerical simulations can.
**I move away from the infinite flat plane to breathe in

Offline somerled

  • *
  • Posts: 112
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #42 on: November 06, 2019, 01:03:23 PM »
Yes hundreds , glad we agree on that - your figure of 100,000s is more specific in that that figure  is a thousand hundreds . Wasn't it you that specified the solar system as a 10 body problem ?

I don't suggest anything about the atmosphere and it is chaos theory and the n-body problem which suggests the solar system is unstable .

Numerical simulations are not solutions to problems . They are simulations that is all . A computer may model an orbit but that won't be reality . In order to calculate an n-body orbit then all n-variable initial conditions must be known exactly - which we can never know , and this is why the problem is unsolvable .

Not even asteroid 2003 etc orbit is calculable , although you may simulate the orbit numerically . If we can't see ass2003 with the naked eye then how can we ,by observation , tell you where it will be in 50yrs ?

Offline ChrisTP

  • *
  • Posts: 441
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #43 on: November 06, 2019, 01:42:33 PM »
Not being able to solve it isn't the same as it being impossible. If you use software to run a 3d simulation and throw a few hundred smaller balls vaguely in the direction of a ball with more mass you'll probably find at least some of them will start orbiting, right? This is basically the same thing. In all the chaos of the universe things have settled into an orbit by chance. in fact the more bodies there are in the universe the more chance of this happening.

People are assuming the few bodies in our solar system are the only bodies that were somehow made and thrown into a perfect orbit but it was more like a shotgun effect. throw enough objects at a sun and some will start to orbit just the same as if you throw a hundred of small marbles at a small hole in the wall, some may manage to get into the hole but most may not. That doesn't mean that the ones that managed to go into the hole were an impossibilty.
Tom is wrong most of the time. Hardly big news, don't you think?

Re: What are the (flat Earth) stars?
« Reply #44 on: November 06, 2019, 01:53:07 PM »
I am unsure what further explanation you seek.

The atmoplane is certainly never in a state of 100 percent chaos, although there is 100 percent chaos in portions of the atmoplane at any given time.

Certain places experience direct blackouts at high noon, certainly occluding sunlight thousands of miles away.
For instance, what in FE theory accounts for these direct blackouts?  What is doing the occluding and how is it doing it?
Same thing as RE theory, I guess.

Direct blackouts can occur when severe thunderstorms strike an area.

Offline somerled

  • *
  • Posts: 112
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #45 on: November 06, 2019, 02:54:57 PM »
Not being able to solve it isn't the same as it being impossible. If you use software to run a 3d simulation and throw a few hundred smaller balls vaguely in the direction of a ball with more mass you'll probably find at least some of them will start orbiting, right? This is basically the same thing. In all the chaos of the universe things have settled into an orbit by chance. in fact the more bodies there are in the universe the more chance of this happening.

People are assuming the few bodies in our solar system are the only bodies that were somehow made and thrown into a perfect orbit but it was more like a shotgun effect. throw enough objects at a sun and some will start to orbit just the same as if you throw a hundred of small marbles at a small hole in the wall, some may manage to get into the hole but most may not. That doesn't mean that the ones that managed to go into the hole were an impossibilty.

Software is a set of instructions directing your computer to give the required answer . Simulations are not the same thing as reality . Heliocentric system is chaotic by that models prediction , as is the gravitational universe . Reality is different though .  We cannot predict planetary orbit in the heliocentric model .

Offline ChrisTP

  • *
  • Posts: 441
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #46 on: November 06, 2019, 03:23:59 PM »
Not being able to solve it isn't the same as it being impossible. If you use software to run a 3d simulation and throw a few hundred smaller balls vaguely in the direction of a ball with more mass you'll probably find at least some of them will start orbiting, right? This is basically the same thing. In all the chaos of the universe things have settled into an orbit by chance. in fact the more bodies there are in the universe the more chance of this happening.

People are assuming the few bodies in our solar system are the only bodies that were somehow made and thrown into a perfect orbit but it was more like a shotgun effect. throw enough objects at a sun and some will start to orbit just the same as if you throw a hundred of small marbles at a small hole in the wall, some may manage to get into the hole but most may not. That doesn't mean that the ones that managed to go into the hole were an impossibilty.

Software is a set of instructions directing your computer to give the required answer . Simulations are not the same thing as reality . Heliocentric system is chaotic by that models prediction , as is the gravitational universe . Reality is different though .  We cannot predict planetary orbit in the heliocentric model .
Yes, thats why I used the marble example as well. if I'm holding a handful of marbles and I throw them at a wall with a hole in, some may go in. Can you pre-calculate which marbles will go exactly where and how many would go into the hole? If not, does that make it impossible for the that some may go in? The answer is obviously you cannot calculate this, and it's obviously still possible. Just as we can't fully calculate perfectly our solar system, yet that doesn't make it impossible.

"we can't solve the n-body problem so there's no way gravity and orbiting is possible" is a terrible argument I see a lot around here. Mind you mostly from TomB. What we can do in the marbles case is invent a machine (a gun) that is mechanically nearly perfectly made wit hthe exact calculations to shoot marbles into the hole perfectly. This isnt much different from how we can calculate exactly the kind of forces needed to put a rocket into orbit.
Tom is wrong most of the time. Hardly big news, don't you think?

*

Offline Tom Bishop

  • Zetetic Council Member
  • **
  • Posts: 6522
  • Flat Earth Believer
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #47 on: November 06, 2019, 03:47:24 PM »
The availiable solutions for the Three Body Problem are very limited, need to be highly symmetrical and require at least two of the three bodies to be of the same mass.

https://web.archive.org/web/20191010222453/https://arxiv.org/pdf/1709.04775.pdf

The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum  -- At the bottom of p.1 see   “ Therefore, without loss of generality, we consider m1 = m2 = 1 and m3 is varied. ”

https://web.archive.org/web/20191010222522/https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/

Infamous three-body problem has over a thousand new solutions  -- “ Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit. But these new orbits rely on conditions that are somewhere between unlikely and impossible for a real system to satisfy. In all of them, for example, two of the three bodies have exactly the same mass and they all remain in the same plane. ”

https://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993

Over a thousand new periodic orbits of a planar three-body system with unequal masses  -- “ Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass. ”

Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”

Where are the solutions with bodies of different masses?

These systems are rediculous and are nothing like what is proposed by astronomy. Most configurations will fly apart or collapse. Not all combinations of systems stay together. If you guys are going to argue that the Three Body Problem can simulate the systems of astronomy then you will need to show and demonstrate, rather than providing speculation.
« Last Edit: November 06, 2019, 04:10:10 PM by Tom Bishop »

*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #48 on: November 06, 2019, 06:47:54 PM »
Yes hundreds , glad we agree on that - your figure of 100,000s is more specific in that that figure  is a thousand hundreds . Wasn't it you that specified the solar system as a 10 body problem ?

I don't suggest anything about the atmosphere and it is chaos theory and the n-body problem which suggests the solar system is unstable .

Numerical simulations are not solutions to problems . They are simulations that is all . A computer may model an orbit but that won't be reality . In order to calculate an n-body orbit then all n-variable initial conditions must be known exactly - which we can never know , and this is why the problem is unsolvable .

Not even asteroid 2003 etc orbit is calculable , although you may simulate the orbit numerically . If we can't see ass2003 with the naked eye then how can we ,by observation , tell you where it will be in 50yrs ?
I didn't quite understand your answer - do you understand that the atmosphere is also an analytically unsolvable n-body problem or not?

A numerical simulation can predict where an asteroid will be in 50 years with a known error. As it turns out, the solar system is 'calm' enough such that you can predict the position of any body within the solar system to very high accuracy for the next at least 100 years, probably a lot more.

Just to try and open your eyes, here's something to think about: can you tell me of any physical system that is analytically (i.e. exactly) solvable? You'll find that there are almost 0 problems in Physics that are analytically solvable. It's just a reality of the complex world we live in.
**I move away from the infinite flat plane to breathe in

*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #49 on: November 06, 2019, 07:00:29 PM »
These systems are rediculous and are nothing like what is proposed by astronomy. Most configurations will fly apart or collapse. Not all combinations of systems stay together. If you guys are going to argue that the Three Body Problem can simulate the systems of astronomy then you will need to show and demonstrate, rather than providing speculation.
I've talked with you about this before. This post really demonstrates that you don't understand what's being talked about. Nobody is arguing that there are analytical solutions to the n-body problem, as you are implying.
I think you need to do some research on the basics of numerical integration and how it is different from an analytic solution before you comment again.

And as for a demonstration, just look up NASA's Horizons catalogue and you'll see that it has very accurate orbital information about hundreds of thousands of bodies in the solar system, all by using numerical integration.
Are you now going to argue that these numerical calculations that demonstrably very accurately match real life are somehow invalid?
**I move away from the infinite flat plane to breathe in

*

Offline Tom Bishop

  • Zetetic Council Member
  • **
  • Posts: 6522
  • Flat Earth Believer
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #50 on: November 06, 2019, 07:12:58 PM »
Those are numerical simulations that I quoted.

Quote
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”

Again, where can we find numerical simulations with different masses other than your statement that they exist?

Your reference to the NASA models are questionable, as they are using perturbation methods.
« Last Edit: November 06, 2019, 07:30:35 PM by Tom Bishop »

*

Offline BillO

  • *
  • Posts: 513
  • Huh?
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #51 on: November 06, 2019, 07:52:12 PM »
These systems are rediculous and are nothing like what is proposed by astronomy. Most configurations will fly apart or collapse. Not all combinations of systems stay together. If you guys are going to argue that the Three Body Problem can simulate the systems of astronomy then you will need to show and demonstrate, rather than providing speculation.
I've talked with you about this before. This post really demonstrates that you don't understand what's being talked about. Nobody is arguing that there are analytical solutions to the n-body problem, as you are implying.
I have to agree here.  Many people do not seem to be able to, or do not wish to, distinguish between analytic solutions arrived at though numerical methods and numerical solutions.  They are completely different.

Numerical solutions to 'N-body' problems are quite accurate and stable, however they take a lot of computing power to run such simulations and have to be run for each defined problem and offer no analytic solution.

Analytic solutions have the advantage of being in teh form of an equation or function are able to be written down and used in further calculations.  The drawback is the overall failure to produce general analytic solutions to 'N' body problems (as well as others) using numerical methods.
Here a quack, there a quack, everywhere a quack quack.

Re: What are the (flat Earth) stars?
« Reply #52 on: November 06, 2019, 08:19:28 PM »
The three body problem is studied in the field of nonlinear ordinary differential equations with initial conditions: bifurcation theory, an exceedingly difficult branch of advanced mathematics.

https://books.google.ro/books?id=YhXnBwAAQBAJ&printsec=frontcover&dq=wiggins+introduction+to&hl=en&sa=X&ved=0ahUKEwj2yPuosdblAhVC3qQKHUXdByMQ6AEIMDAB#v=onepage&q=wiggins%20introduction%20to&f=false

Here are the known facts concerning the three body problem in the context of bifurcation theory:

https://forum.tfes.org/index.php?topic=10175.msg160183#msg160183

https://forum.tfes.org/index.php?topic=14559.msg191038#msg191038

The most intriguing is the discovery made by Professor Robert W. Bass.

Dr. Robert W. Bass

Ph.D. (Mathematics) Johns Hopkins University, 1955 [Wintner, Hartman]
A. Wintner, world's leading authority on celestial mechanics
Post-Doctoral Fellow Princeton University, 1955-56 [under S. Lefschetz]
Rhodes Scholar
Professor, Physics & Astronomy, Brigham Young University

"In a resonant, orbitally unstable or "wild" motion, the eccentricities of one or more of the terrestrial planets can increase in a century or two until a near collision occurs. Subsequently the Principle of Least Interaction Action predicts that the planets will rapidly "relax" into a configuration very near to a (presumably orbitally stable) resonant, Bode's-Law type of configuration. Near such a configuration, small, non-gravitational effects such as tidal friction can in a few centuries accumulate effectively to a discontinuous "jump" from the actual phase-space path to a nearby, truly orbitally stable, path. Subsequently, observations and theory would agree that the solar system is in a quasi-periodic motion stable in the sense of Laplace and orbitally stable. Also, numerical integrations backward in time would show that no near collision had ever occurred. Yet in actual fact this deduction would be false."

"I arrived independently at the preceding scenario before learning that dynamical astronomer, E. W. Brown, president of the American Astronomical Society, had already outlined the same possibility in 1931."

Dr. Robert Bass, Stability of the Solar System:

https://web.archive.org/web/20120916174745/http://www.innoventek.com:80/Bass1974PenseeAllegedProofsOfStabilityOfSolarSystemR.pdf

Dr. E.W. Brown

Fellowship, Royal Society
President of the American Mathematical Society
Professor of Mathematics, Yale University
President of the American Astronomical Society

What this means is that the interval of assured reliability for Newton's equations of gravitational motion is at most three hundred years.

If any proofs can be provided that the solar system underwent cataclysmic planetary collisions in recent historical times, this fact would render any kind of heliocentric orbital calculations as completely useless.

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1936055#msg1936055 (part I)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938384#msg1938384 (part II)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938393#msg1938393 (part III)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938396#msg1938396 (part IV)


*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #53 on: November 06, 2019, 10:05:56 PM »
Those are numerical simulations that I quoted.

Quote
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”

Again, where can we find numerical simulations with different masses other than your statement that they exist?

Your reference to the NASA models are questionable, as they are using perturbation methods.
You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a user-specified time span less than 200 years."
"and are then numerically integrated on-demand by Horizons to other times of interest"

Need I go on?
**I move away from the infinite flat plane to breathe in

*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #54 on: November 06, 2019, 10:11:54 PM »
Those are numerical simulations that I quoted.
Your opening line was "The availiable solutions for the Three Body Problem are very limited..." and then you go on to say "Where are the solutions with bodies of different masses?"

There are limited analytic solutions to the three-body problem. There are no general analytic solutions to the three-body problem with arbitrary masses.

I'm talking about numerical solutions, not analytic solutions. Whether there is an analytic solution to the three-body problem is entirely irrelevant - what matters is the thing we're actually discussing, which is the accuracy of the numerical solution.

P.S. do you have any coding experience? You can just open python or matlab etc. yourself and use pre-made and easy to use numerical integration algorithms, chuck in initial conditions for e.x. the solar system and see what happens.
« Last Edit: November 06, 2019, 10:15:58 PM by Tim Alphabeaver »
**I move away from the infinite flat plane to breathe in

*

Offline Tom Bishop

  • Zetetic Council Member
  • **
  • Posts: 6522
  • Flat Earth Believer
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #55 on: November 06, 2019, 11:33:09 PM »
I don't understand. Who was talking about analytical solutions? Those are numerical solutions that I linked you to:

Quote
https://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993

Over a thousand new periodic orbits of a planar three-body system with unequal masses  -- “ Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass.

Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a "clean numerical simulation"

Now, where can we find examples of numerical three body problem solutions with bodies of different masses?

Sandokhan, do you know where we can find them?

You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a user-specified time span less than 200 years."
"and are then numerically integrated on-demand by Horizons to other times of interest"

Need I go on?

From your link:

Quote
Comet and asteroid ephemerides are integrated from initial conditions called "osculating elements". These describe the 3-dimensional position and velocity of the body at a specific time. The integrator starts with this state and takes small time steps, summing the perturbing forces at each step before taking another step. A variable order, variable step-size integrator is used to control error growth. In this way, the gravitational attraction of other major solar system bodies on the target body trajectory is taken into account.

Summing of perturbing forces?

This sounds like what Dr. Gopi Krishna Vijaya is explaining in his Replacing the Foundations of Astronomy paper:

https://reciprocalsystem.org/PDFa/Replacing%20the%20Foundations%20of%20Astronomy%20(Vijaya,%20Gopi%20Krishna).pdf

Quote
Epicycles Once More

Following the Newtonian era, in the 18th century there were a series of mathematicians – Bernoulli, Clairaut, Euler, D’Alembert, Lagrange, Laplace, Leverrier – who basically picked up where Newton left off and ran with it. There were no descendants to the wholistic viewpoints of Tycho and Kepler, but only those who made several improvements of a mathematical nature to Newtonian theory. Calculus became a powerful tool in calculating the effects of gravitation of all the planets upon each other, due to their assumed masses. The motion of the nearest neighbor – the Moon – was a surprisingly hard nut to crack even for Newton, and several new mathematical techniques had to be invented just to tackle that.

In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise:



In other words, the entire thought process took several steps backwards, to redo the same process as the Ptolemaic - Copernican epicycle theory, only with different variables. The more logical way of approach would have been to redirect the focus of the improved mathematical techniques to the assumptions in Newton’s theory, but instead the same equations were re-derived with calculus, without examining the assumptions. Hence any modern day textbook gives the same derivation for circular and elliptical motion that Newton first derived in his Principia. The equivalence of the epicycle theory and gravitational theory has not been realized, and any new discovery that fits in with the mathematical framework of Newtonian gravity is lauded as a “triumph of the theory of gravitation.” In reality, it is simply the triumph of fitting curves to the data or minor linear extrapolations – something that had already been done at least since 2nd century AD. Yet the situation is conceptually identical.

~

The Dead End

In the late 19th century, one of the French mathematicians – Henri Poincaré – had already discovered that many of the terms being used in the “perturbation” series by mathematicians like Laplace and Lagrange were becoming infinite for long periods of time, making the system unstable. In simple words, the solutions ‘blow up’ fairly quickly. He also showed that the general problem of 3 mutually gravitating bodies was insoluble through any mathematical analysis! Many physicists and mathematicians built up modern “Chaos theory” based on these ideas, to show simply that one cannot calculate the movements of the planets accurately. Thus began the field of non-linear dynamics.

In the middle of the 20th century, with computers entering the field, the mathematicians pretty much gave up on calculating the orbits by themselves and programmed the computer to do it, even though it was mathematically shown that these orbits were incalculable. They had to be satisfied with approximations or numerical methods (or “brute force” methods.) The result of it all was that after 300 years, Newtonian/Einsteinian thought lands in the same spot that Kepler ended: the orbits point to a living or chaotic system. Only now, there is the additional baggage of all the wrong concepts introduced with regard to “inverse-square law”, “gravitational attraction”, “gravitational mass” and “curved space-time” along with uncountable number of minor assumptions. In this process, an enormous amount of human effort was put to derive thousands of terms in equations over centuries. The entire enterprise has been a wild goose chase
« Last Edit: November 07, 2019, 02:59:28 AM by Tom Bishop »

*

Offline BillO

  • *
  • Posts: 513
  • Huh?
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #56 on: November 07, 2019, 12:07:07 AM »
Now, where can we find examples of numerical three body problem solutions with bodies of different masses?
I gave you one about a year ago  (or so).


Sandokhan, do you know where we can find them?
LOL!
Here a quack, there a quack, everywhere a quack quack.

Re: What are the (flat Earth) stars?
« Reply #57 on: November 07, 2019, 08:56:04 AM »
One of the best accounts of the numerical methods applied to solar system stability questions:

http://immanuelvelikovsky.com/NewtonEinstein&Veli.pdf (chapter 3, Solar System Instability, pg 84 - 112, especially pg 97, 103-111)

*

Offline BillO

  • *
  • Posts: 513
  • Huh?
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #58 on: November 07, 2019, 01:56:55 PM »
Really?  I've read that book.  It is solely based on the ramblings of Velikovsky, the poster child for pseudoscience.  There is no mathematical models in it, either numercalyy simulated or analytical arrived at though numerical methods.

Page 97 in particular deals with the stability of a solar system in a universe full of massive rogue bodies that would surely perturb the orbits of all the planets.  Well, the fact is that, whether the universe is full of massive rogue bodies or not, none have been witnessed in our time to have perturbed anything.

But enough of that.  Briefly at the top of the page is a quote that mentions the instability in an analytic solution arrived at through numerical methods.  This is something we don't have to go to rubbish like the Velikovskian to know about.   Every 1st year mechanics (an I mean the branch of physics here, not fixing cars) student learns about the failure of numerical methods to provide a solution to the 'N-body' problem.  I actually think Tom was asking for a reference for a numerical solution, not an analytic solution arrived at through numerical methods.  Again, there is a huge difference.
Here a quack, there a quack, everywhere a quack quack.

Re: What are the (flat Earth) stars?
« Reply #59 on: November 07, 2019, 02:24:40 PM »
The book is written by Charles Ginenthal, one of the top scholars in the world.

Basically, what Velikovsky proposed is that electrical and magnetic forces must be included in celestial mechanics.

And he was right.

Here is the exact formula for the BIEFELD-BROWN EFFECT:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2177793#msg2177793





This is the Weyl-Majumdar-Papapetrou-Ivanov solution.


https://arxiv.org/pdf/gr-qc/0507082.pdf

Weyl electrovacuum solutions and gauge invariance
Dr. B.V. Ivanov

https://arxiv.org/pdf/gr-qc/0502047.pdf

On the gravitational field induced by static electromagnetic sources
Dr. B.V Ivanov


Here is how the solution was derived in 1917 by Hermann Weyl, a physicists several ranks higher than Einstein:

http://www.jp-petit.org/papers/cosmo/1917-Weyl-en.pdf


If you do not like Velikovsky, then you are going to be enthralled by Kepler, who FAKED/FUDGED the entire set of data for the Nova Astronomia:

https://forum.tfes.org/index.php?topic=10175.msg160186#msg160186

https://forum.tfes.org/index.php?topic=10175.msg160200#msg160200


Here is an analysis of Jacques Laskar's numerical approach using only mainstream sources:

https://forum.tfes.org/index.php?topic=10175.msg160189#msg160189


Chapter 3 from Newton, Einstein & Velikovsky includes the references on numerical methods, a sure sign you did not read it at all.

https://arxiv.org/pdf/0708.2875.pdf

http://www.cs.toronto.edu/~wayne/research/papers/nphys728-published.pdf


http://immanuelvelikovsky.com/NewtonEinstein&Veli.pdf (chapter 3, Solar System Instability, pg 84 - 112, especially pg 97, 103-111) - these pages include a formidable analysis of the assumptions made by physicists who employ various kinds of numerical algorithsm to study celestial mechanics)